[Paper Review] Global QCD Analysis of Pion Parton Distributions with Threshold Resummation

Barry, P. C., Ji, Chueng-Ryong+2 more|arXiv (Cornell University)|Aug 12, 2021

Quantum Chromodynamics and Particle Interactions68 citations

TL;DR

This study presents the first global QCD analysis of pion parton distributions using a Bayesian Monte Carlo framework with next-to-leading logarithmic (NLL) threshold resummation in Drell-Yan processes. It finds that threshold resummation significantly alters the valence quark distribution's large-x behavior, with βv ranging from ≈1 to >2.5, and increases the gluon momentum fraction to ≈40%, contributing ≈40 MeV to the pion mass.

ABSTRACT

We perform the first global QCD analysis of pion valence, sea quark, and gluon distributions within a Bayesian Monte Carlo framework with threshold resummation on Drell-Yan cross sections at next-to-leading log accuracy. Exploring various treatments of resummation, we find that the large-$x$ asymptotics of the valence quark distribution $\sim (1-x)^{\beta_v}$ can differ significantly, with $\beta_v$ ranging from $\approx 1$ to $> 2.5$ at the input scale. Regardless of the specific implementation, however, the resummation induced redistribution of the momentum between valence quarks and gluons boosts the total momentum carried by gluons to $\approx 40\%$, increasing the gluon contribution to the pion mass to $\approx 40$ MeV.

Motivation & Objective

• To perform a global QCD analysis of pion parton distributions (PDFs) including threshold resummation effects at NLL accuracy.
• To investigate how different resummation prescriptions—Mellin-Fourier (MF) and double Mellin (DM)—affect the large-x behavior of the valence quark PDF.
• To quantify the impact of threshold resummation on the momentum partitioning between valence quarks and gluons in the pion.
• To constrain the pion's gluon and sea quark distributions using Drell-Yan and leading neutron (LN) electroproduction data within a Bayesian framework.
• To assess the contribution of gluons to the pion mass via the resummed PDFs.

Proposed method

• Employing a Bayesian Monte Carlo framework to perform a global fit to Drell-Yan and LN electroproduction data.
• Applying next-to-leading logarithmic (NLL) threshold resummation using the Mellin-Fourier (MF) and double Mellin (DM) methods to resum large logarithms from soft gluon emissions.
• Solving DGLAP evolution equations in Mellin space to ensure numerical stability and avoid singularities from the Landau pole.
• Using the resummed hard coefficients in conjugate space (Mellin and Fourier transforms) to compute the hadronic cross sections.
• Inverting the Mellin-Fourier transformed cross sections back to momentum space for comparison with experimental data.
• Fixing the sea quark and gluon PDFs at the input scale based on earlier analyses, while allowing the valence quark PDF to be constrained by data.

Experimental results

Research questions

• RQ1 How does threshold resummation at NLL accuracy affect the large-x behavior of the pion valence quark PDF?
• RQ2 What is the impact of different resummation prescriptions (MF vs. DM) on the effective βv parameter in the (1−x)^βv ansatz?
• RQ3 To what extent does threshold resummation redistribute momentum from valence quarks to gluons in the pion?
• RQ4 What is the resulting contribution of gluons to the pion mass after including resummation effects?
• RQ5 How well do the resummed PDFs describe the available Drell-Yan and LN electroproduction data?

Key findings

• Threshold resummation leads to a significant redistribution of momentum, increasing the gluon momentum fraction to approximately 40%.
• The effective βv parameter in the valence quark PDF (1−x)^βv varies widely depending on the resummation prescription, ranging from ≈1 to >2.5 at the input scale.
• The resummed calculation yields a harder valence quark distribution than fixed-order calculations, with βv values approaching 2 even when the fixed-order fit suggests βv ≈1.
• The gluon contribution to the pion mass is estimated at ≈40 MeV, highlighting the importance of non-perturbative gluonic effects.
• The double Mellin (DM) method provides a more stable and consistent framework for resummation compared to the traditional MF method.
• The inclusion of threshold resummation improves the description of high-x Drell-Yan and LN data, particularly in the threshold region where fixed-order calculations fail.